# Banking Crisis Sign Flip Probe

Why does old_dep → banking risk in non-OECD but not OECD?

## Part 1: Confirm Sign Flip

| Sample | old_dep coef | p | youth_dep coef | p | N | Countries |
|:---|---:|---:|---:|---:|---:|---:|
| Full | +0.075 | 0.016** | +0.017 | 0.095* | 6,419 | 174 |
| OECD | +0.000 | 0.996 | +0.093 | 0.120 | 1,475 | 37 |
| Non-OECD | +0.095 | 0.035** | +0.026 | 0.009*** | 4,944 | 137 |

Confirmed: old_dep positive and significant in non-OECD (p=0.035), null in OECD.

## Part 2: Is It Just Income?

| Model | old_dep | p | old_dep×log_gdp_pc | p |
|:---|---:|---:|---:|---:|
| Non-OECD + GDP/pc | +0.100 | 0.021** | — | — |
| Non-OECD + interaction | +1.504 | 0.003*** | -0.138 | 0.005*** |
| OECD + GDP/pc | -0.076 | 0.430 | — | — |
| OECD + interaction | -2.686 | 0.155 | +0.245 | 0.167 |

**Key finding**: GDP/pc does NOT absorb old_dep in non-OECD (survives at p=0.021). The interaction is strongly significant (-0.138, p=0.005): the aging→banking risk effect **weakens as income rises**. At low GDP/pc, old_dep effect is very large (+1.50); it diminishes toward zero at higher income levels.

## Part 3: Income Tercile Split (Non-OECD)

| Tercile | old_dep coef | p | youth_dep | p | N | Countries |
|:---|---:|---:|---:|---:|---:|---:|
| Low (<$4,840) | +0.560 | 0.018** | +0.049 | 0.019** | 1,719 | 44 |
| Mid ($4,840-$13,678) | +0.090 | 0.152 | -0.024 | 0.191 | 1,284 | 46 |
| High (>$13,678) | -0.136 | 0.245 | +0.027 | 0.333 | 963 | 42 |

**The effect is entirely concentrated in low-income non-OECD** (old_dep=+0.56, p=0.018). Middle and high income non-OECD show null or negative old_dep. This is NOT "aging populations are risky" — it's "poor countries with slightly older populations face banking stress."

## Part 4: Financial Depth Proxies

| Model (Non-OECD) | old_dep | p | Interaction | p |
|:---|---:|---:|---:|---:|
| + Gross liabilities | +0.093 | 0.042** | — | — |
| + Gross liab interaction | +0.117 | 0.019** | -0.0001 | 0.233 |
| + Trade openness | +0.074 | 0.130 | — | — |
| + Trade interaction | +0.122 | 0.155 | -0.0004 | 0.499 |
| + FX reserves | +0.097 | 0.033** | — | — |
| + Reserves interaction | +0.178 | 0.003*** | -0.0031 | 0.036** |

**FX reserves interaction significant** (-0.003, p=0.036): countries with higher reserves buffer the aging→banking risk. Trade openness marginally absorbs old_dep (drops to p=0.13). Gross liabilities don't matter.

## Part 5: Pension Spending (OECD only — only 4 non-OECD countries have data)

| Model (OECD) | old_dep | p | pension_spending | p |
|:---|---:|---:|---:|---:|
| + Pension | -0.063 | 0.530 | +0.0003 | 0.742 |
| + Pension interaction | -0.257 | 0.249 | -0.001 | 0.470 |

All null in OECD. Cannot test pension mechanism in non-OECD due to data limitations.

## Part 6: Z Polynomial

| Sample | Z₁ | p | Z₂ | p | Z₃ | p |
|:---|---:|---:|---:|---:|---:|---:|
| Non-OECD | -0.109 | 0.137 | +0.013 | 0.255 | -0.0004 | 0.406 |
| Non-OECD + GDP/pc | -0.037 | 0.629 | +0.003 | 0.798 | -0.00001 | 0.981 |
| OECD | -0.927 | 0.004*** | +0.121 | 0.006*** | -0.004 | 0.009*** |

Z polynomial is completely null in non-OECD (old_dep is the relevant demographic variable there). Z is strongly significant in OECD with the expected negative sign (aging → fewer crises).

## Interpretation

The non-OECD old_dep→banking risk is **a low-income phenomenon, not an aging phenomenon**:

1. Entirely concentrated in countries below $4,840 GDP/capita
2. Weakens monotonically with income (interaction p=0.005)
3. Likely mechanism: in very poor countries, a slightly older population (old_dep moving from ~3% to ~6%) strains rudimentary banking systems that lack deposit insurance, pension coverage, and reserves buffers
4. FX reserves moderate the effect (p=0.036) — consistent with lack of institutional buffers
5. Not the same mechanism as OECD aging at all — comparing old_dep=0.04 in Niger to old_dep=0.30 in Japan

**Recommendation**: The paper should characterize this as "demographic stress in low-income banking systems" rather than "aging causes banking crises in developing countries." The OECD story (aging is protective via Z polynomial) and the non-OECD story (modest aging strains weak institutions) are fundamentally different phenomena that happen to share a demographic variable.
